TY - JOUR

T1 - Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

AU - Schneide, Christiane

AU - Pandey, Ambrish

AU - Padberg-Gehle, Kathrin

AU - Schumacher, Jörg

PY - 2018/11/15

Y1 - 2018/11/15

N2 - We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr =0.7, a Rayleigh number Ra =105, and an aspect ratio Γ=16 is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem et al. [Phys. Rev. E 93, 063107 (2016)2470-004510.1103/PhysRevE.93.063107], builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τL and lengths λUL of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, τ and λU, respectively. This trajectory-based clustering is found to work for times tτ≈τL. Longer time periods tτL require a change of the analysis method to a density-based trajectory clustering by means of time-averaged Lagrangian pseudotrajectories, which is applied in this context for the first time. A small coherent subset of the pseudotrajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.

AB - We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr =0.7, a Rayleigh number Ra =105, and an aspect ratio Γ=16 is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem et al. [Phys. Rev. E 93, 063107 (2016)2470-004510.1103/PhysRevE.93.063107], builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τL and lengths λUL of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, τ and λU, respectively. This trajectory-based clustering is found to work for times tτ≈τL. Longer time periods tτL require a change of the analysis method to a density-based trajectory clustering by means of time-averaged Lagrangian pseudotrajectories, which is applied in this context for the first time. A small coherent subset of the pseudotrajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.

KW - Mathematics

UR - http://www.scopus.com/inward/record.url?scp=85057985476&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.3.113501

DO - 10.1103/PhysRevFluids.3.113501

M3 - Journal articles

AN - SCOPUS:85057985476

VL - 3

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 11

M1 - 113502

ER -